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Job No. Sheet No. Rev.
Job Title
XX
Material Properties
Characteristic strength of concrete, fcu (≤ 60N/mm2; HSC N/A) 25 N/mm2 OK
Yield strength of longitudinal steel, fy 460 N/mm2
Yield strength of shear link steel, fyv 460 N/mm2
Type of concrete and density, ρc 24 kN/m3
Stair Structural Scheme
Stair structural scheme
Scheme 1 Stair spanning longitudinally simply supported with SDL on elevation over width b
Scheme 2 Stair spanning horizontally cantilever with SDL on elevation at free end
Scheme 3 Stair spanning horizontally simply supported without SDL on elevation
Insitu (landing starters) or precast (mid section shear connection) (applicable to scheme 1 only)
Breadth of supporting member at one end (applicable to scheme 1 only), lb,1 0.150 m
Breadth of supporting member at the other end (applicable to scheme 1 only), l 0.150 m
Stair Parameters
Bottom landing 150 mm thick
Top landing 150 mm thick
Point A 0 mm to the left
Point B 0 mm to the left
Use of stair
rmax gmin
Private stair 220 220 mm
Institutional and assembly stair 180 280 mm
Other stair 190 250 mm
Slope angle of stair, θ (<=42°) 32.5 degrees OK
Rise of stair, H 1.750 m
Number of risers, Nriser 10
Height of riser, r = H/Nriser (<=rmax) 175 mm OK
Number of goings, Ngoing = Nriser + No. of offset goings 12
Length of going, g = r/tanθ (>=gmin) 275 mm OK
Span of stair, L = Ngoing.g 3.300 m
Effective span of stair (applicable to scheme 1 only), Leff = L+0.5(MIN(lb1,1.8m)+MIN(l3.450 m
Stair flight L occupies at least 60% of stair effective span Leff (applicable to scheme 1 only) ?Yes
Parameter 2r+g (>=550mm, <=700mm) 625 mm OK
Slope length of stair, q = √(L2+H2) 3.735 m
Depth of waist, h 150 mm
Width of stair, b 1.200 m
Member Design - RC Staircase 19-08-15
Engineering Calculation Sheet Consulting Engineers jXXX 1
Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx
CONSULTING
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Made by Date Chd.
Drg. Ref.
Member/Location
L
Hr
gh
Structural Landing
Structural Landing
Point A
Point B
The start of a flight (firstrise) and the end of theprevious flight (lastgoing) may be set outstaggered by:-1. 0 going2. 1 going3. 2 goingsThis merely increases thestair flight span by theabove goings.
Job No. Sheet No. Rev.
Job Title
XX
Cover to all reinforcement, cover (usually MAX(25, φ) internal; 40 external) 25 mm
Effective depth to sagging steel, ds 119 mm
Scheme 1 d s = h - cover - φ s /2 119 mm
Scheme 2 d s = (r.L/ q + h - cover - φ s /2)/2 N/A mm
Scheme 3 d s = (r.L/ q + h - cover - φ s /2)/2 N/A mm
Effective depth to hogging steel, dh 119 mm
Scheme 1 d h = h - cover - φ h /2 119 mm
Scheme 2 d h = h. q/L + r/2 - cover - φ h /2 N/A mm
Scheme 3 d h = h. q/L + r/2 - cover - φ h /2 N/A mm
Sagging steel reinforcement diameter, φs 12 mm
Sagging steel reinforcement pitch, ps 175 mm
Sagging steel area provided, As,prov,s = (π.φs2/4)/ps 646 mm2/m
Hogging steel reinforcement diameter, φh 12 mm
Hogging steel reinforcement pitch, ph 175 mm
Hogging steel area provided, As,prov,h = (π.φh2/4)/ph 646 mm2/m
Shear link diameter, φlink 0 mm
Number of links per metre, nlink 4 /m
Area provided by all links per metre, Asv,prov = nlink.π.φlink2/4 0 mm2/m
Pitch of links, S 200 mm
Stair Loading (Slope Loading)
Live load, LL 4.00 kPa
Superimposed dead load, SDL 1.20 kPa
Dead load of stair (on slope), DL = h.ρc + g.(H/2)/q.ρc 5.15 kPa
ULS stair loading (on slope) excluding SDLelev,stair, ωULS,stair,noSDLelev 15.13 kPa
ω ULS,stair,noSDLelev = 1.4(DL + SDL.(L, H or L+H)/q) + 1.6(LL.L/q)
Note that the loading above is in the vertical direction, however on and along the slope;
Stair Loading (Elevation Loading)
Superimposed dead load on stair (on slope), SDLelev,stair 0.00 kN/m
jXXX 2
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Member Design - RC Staircase
Engineering Calculation Sheet Consulting Engineers
19-08-15
Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsxMade by Date Chd.
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Job No. Sheet No. Rev.
Job Title
XX
Utilisation Summary
Item UT Remark
Sag moment, Ms 79% OK
Hog moment, Mh 38% OK
% Min sag reinforcement 30% OK
% Min hog reinforcement 30% OK
Ultimate shear stress 5% OK
Shear design capacity 31% OK
Deflection utilisation 97% OK
Total utilisation 97% OK
Detailing requirements
% Sagging reinforcement 0.43 %
% Hogging reinforcement 0.43 %
Estimated steel reinforcement quantity (130 − 220kg/m3) 68 kg/m3
[ 7.850 . (A s,prov,s /scheme(h)+A s,prov,h /scheme(h)) ]; No curtailment; No laps; Links ignored; Distribution steel ignored;
Estimated steel reinforcement quantity (130 − 220kg/m3) 108 kg/m3 IStructE
[ 12.5 . (A s,prov,s /scheme(h)+A s,prov,h /scheme(h)) ]; No curtailment; No laps; Links ignored; Distribution steel ignored;
[Note that steel quantity in kg/m3 can be obtained from 125.0 x % rebar];
Material cost: concrete, c 180 units/m3 steel, s 4500 units/tonne
Reinforced concrete material cost = [c+(est. rebar quant).s].scheme(h)100 units/m2
ULS Loading on Supporting Structure
Line shear on supporting structure, RV = V 26 kN/m
Line moment on supporting structure, RM = Mhog N/A kNm/m
Note that for scheme 1, R V is conservatively calculated based on L eff instead of L.
Geometrical Requirements
All geometrical requirements satisfied ? OK
Slope angle of stair, θ OK
Height of riser, r OK
Length of going, g OK
Parameter 2r+g OK
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OK
Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx
Member Design - RC Staircase 19-08-15Made by Date Chd.
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Job No. Sheet No. Rev.
Job Title
XX
Structural Analysis Stair
Sag moment, Msag 24 kNm/m
Scheme 1 M sag = 0.125(ω ULS,stair,noSDLelev+1.4SDL elev,stair /b).q.L eff 24 kNm/m
Scheme 2 M sag = 0.0 N/A kNm/m
Scheme 3 M sag = 0.125ω ULS,stair,noSDLelev .b2 N/A kNm/m
Hog moment, Mhog 12 kNm/m
Scheme 1 Insitu M hog = 0.0625(ω ULS,stair,noSDLelev+1.4SDL elev,stair 12 kNm/m
Precast M hog = 0.0 N/A kNm/m
Scheme 2 M hog = 0.5ω ULS,stair,noSDLelev .b2+1.4SDL elev,stair .b N/A kNm/m
Scheme 3 M hog = 0.0625ω ULS,stair,noSDLelev .b2 N/A kNm/m
Shear, V 26 kN/m
Scheme 1 V = 0.5(ω ULS,stair,noSDLelev+1.4SDL elev,stair /b).L eff 26 kN/m
Scheme 2 V = ω ULS,stair,noSDLelev .b+1.4SDL elev,stair N/A kN/m
Scheme 3 V = 0.5ω ULS,stair,noSDLelev .b N/A kN/m
Note that the effect of the axial force within the stair is ignored, the magnitude of which is presented below;
Axial force, A 13 kN/m
Scheme 1 A = ±0.5(ω ULS,stair,noSDLelev+1.4SDL elev,stair /b).H 13 kN/m
/scheme(h)) ]; No curtailment; No laps; Links ignored; Distribution steel ignored;Scheme 2 A = 0.0 N/A kN/m
Scheme 3 A = 0.0 N/A kN/m
CONSULTING
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Member Design - RC Staircase 19-08-15
Engineering Calculation Sheet Consulting Engineers jXXX 4
Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsxMade by Date Chd.
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Job No. Sheet No. Rev.
Job Title
XX
Stair Moment Design
Sag moment, Msag 24 kNm/m
Hog moment, Mhog 12 kNm/m
Ensure singly reinforced
K' K z As As,prov UT
Sag moment, Msag 0.156 0.069 109 511 646 79% OK
Hog moment, Mhog 0.156 0.034 113 247 646 38% OK
Note β b = 1.00 and K' = 0.156. If K > K', then UT = 999%.
Note that A s and A s,prov above are in units of mm2/m.
% Min sag reinforcement (>= 0.0024bh G250; >= 0.0013bh G460) 0.43 %
Scheme 1 h = h 150 mm
Scheme 2 h = (r.L/ q + h)/2 N/A mm
Scheme 3 h = (r.L/ q + h)/2 N/A mm
% Min sag reinforcement utilisation 30% OK
% Min hog reinforcement (>= 0.0024bh G250; >= 0.0013bh G460) 0.43 %
Scheme 1 h = h 150 mm
Scheme 2 h = h. q/L + r/2 N/A mm
Scheme 3 h = h. q/L + r/2 N/A mm
% Min hog reinforcement utilisation 30% OK
Stair Shear Design
Ultimate shear stress, vult=V/bdh (< 0.8fcu0.5 & 5N/mm2) 0.22 N/mm2
Ultimate shear stress utilisation 5% OK
Design shear stress, vd=V/bdh 0.22 N/mm2
(Conservatively, shear capacity enhancement by either calculating v d at d from support and
comparing against unenhanced v c as clause 3.4.5.10 BS8110 or calculating v d at support and
comparing against enhanced v c within 2d of the support as clause 3.4.5.8 BS8110 ignored;)
Area of tensile steel reinforcement provided, As,prov,h 646 mm2/m
ρw = 100As,prov,h/bdh 0.54 %
vc = (0.79/1.25)(ρwfcu/25)1/3(400/dh)
1/4; ρw<3; fcu<40; (400/dh)1/4>0.67 0.70 N/mm2
Check vd < vc for no links VALID
Concrete shear capacity vc.(bdh) 83 kN/m
Check vc < vd < 0.4 + vc for nominal links N/A
Provide nominal links such that Asv / S > 0.4b/(0.95fyv) i.e. Asv / S > 0.92 mm2/mm/m
Concrete and nominal links shear capacity (0.4 + vc).(bdh) 131 kN/m
Check vd > 0.4 + vc for design links N/A
Provide shear links Asv / S > b(vd-vc)/(0.95fyv) i.e. Asv / S > 0.92 mm2/mm/m
Concrete and design links shear capacity (Asv,prov/S).(0.95fyv).dh + v 83 kN/m
Area provided by all links per metre, Asv,prov 0 mm2/m
Tried Asv,prov / S value 0.00 mm2/mm/m
Design shear resistance utilisation 31% OK
5jXXX
Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx
CONSULTING
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Engineering Calculation Sheet Consulting Engineers
Member Design - RC Staircase 19-08-15
z <=0.95d
Made by Date Chd.
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Job No. Sheet No. Rev.
Job Title
XX
Detailing Requirements
All detailing requirements met ? OK
Max sagging steel reinforcement pitch (<3ds, <750mm) 175 mm OK
Max hogging steel reinforcement pitch (<3dh, <750mm) 175 mm OK
Max sagging steel reinforcement pitch 175 mm OK
Max hogging steel reinforcement pitch 175 mm OK
Min sagging steel reinforcement pitch (>75mm+φs, >100mm+φs if T40) 175 mm OK
Min hogging steel reinforcement pitch (>75mm+φh, >100mm+φh if T40) 175 mm OK
Note an allowance has been made for laps in the min pitch by increasing the criteria by the bar diameter.
% Max sagging reinforcement (<= 0.04bh) 0.43 % OK
% Max hogging reinforcement (<= 0.04bh) 0.43 % OK
Sagging steel reinforcement diameter, φs (>=10mm) 12 mm OK
Hogging steel reinforcement diameter, φh (>=10mm) 12 mm OK
CONSULTING
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Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx
Member Design - RC Staircase 19-08-15Made by Date Chd.
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Job No. Sheet No. Rev.
Job Title
XX
Deflection Criteria
Span, l 3.450 m
Scheme 1 l = L eff 3.450 m
Scheme 2 l = b N/A m
Scheme 3 l = b N/A m
Span, l / effective depth, d ratio 29.0
Scheme 1 l/d = l/d s 29.0
Scheme 2 l/d = l/d h N/A
Scheme 3 l/d = l/d s N/A
Basic span / effective depth ratio criteria 20.0
Scheme 1 Basic l/d = 20 20.0
Scheme 2 Basic l/d = 7 N/A
Scheme 3 Basic l/d = 20 N/A
Multiplier C1,span more or less than 10m 1.00
Modification factor for tension C2
M/bd2 1.72 N/mm2
Scheme 1 M/bd2 = M sag /bd s
2 1.72 N/mm2
Scheme 2 M/bd2 = M hog /bd h
2 N/A N/mm2
Scheme 3 M/bd2 = M sag /bd s
2 N/A N/mm2
(βb=1.0) 243 N/mm2
Scheme 1 As,req/As,provsag 0.79
Scheme 2 As,req/As,provhog N/A
Scheme 3 As,req/As,provsag N/A
Modification 1.30
Modification factor for tension C3 = 1.15 if stair flight L occupies at least 60% of stair effective span Leff (applicable to scheme 1 only) 1.15
Modified span / effective depth ratio criteria 29.8
Deflection utilisation 97% OK
CONSULTING
E N G I N E E R S 7
Engineering Calculation Sheet Consulting Engineers jXXX
Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx
Member Design - RC Staircase 19-08-15Made by Date Chd.
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Scheme Design
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Member Design - RC Staircase 19-08-15
jXXX 8
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Typical Initial Span / Effective Depth Ratios
Member Design - RC Staircase 19-08-15
Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx
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Standard Critical Dimensions Details
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Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx
10jXXX
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The rise should not be more than 220mm and the going (tread less nosing) no less than 220mm. Thepitch should be no steeper than 42 degrees so the minimum going cannot be used with the maximumrise. A good guide is that twice the rise plus the going (2R+G) should be between 550mm and 700mm.The width of the stair should not be less than 600mm if leading to one room or 800mm if leading totwo rooms. The clear headroom of at least 2m should be provided. Handrails should be 900mmabove the pitch line minimum. Landings are required at the top and bottom of each flight. They shouldbe at least as wide and long as the stair width.
Job No. Sheet No. Rev.
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XX
Engineering Calculation Sheet Consulting Engineers jXXX
19-08-15Member Design - RC Staircase
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Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx
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Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx
Member Design - RC Staircase
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Standard Insitu Concrete Staircase Reinforcement Details (Scheme 1)
Member Design - RC Staircase 19-08-15
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Engineering Calculation Sheet Consulting Engineers jXXX
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Standard Insitu Concrete Staircase Reinforcement Details (Scheme 2)
Engineering Calculation Sheet Consulting Engineers
19-08-15
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Member Design - RC Staircase
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Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx
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Member Design - RC Staircase 19-08-15Made by Date Chd.
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Standard Insitu Concrete Staircase Details
Member Design - RC Staircase 19-08-15
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XX 19-08-15
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Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx
Member Design - RC Staircase
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CONSULTING
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CONSULTING
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Member Design - RC Staircase 19-08-15
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Standard Precast Concrete Staircase Details
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Standard Construction Method Details
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